Service is regarded as the most crucial shot in tennis matches, and hence affects the outcome. This study aims to construct a mathematical model that expresses the scoring probability of service shots. Here, "scoring" means that the server wins points in subsequent rallies after a service. The explanatory variables are the service landing location and the ranking points of the players (logarithms of ranking points for the two players). The model construction method is a stepwise regression of the generalized linear model. The model is constructed using more than 110,000 service shots from Association of Tennis Professionals Tour tournaments of 2019. The model comprises four service situations: first/second and ad/deuce sides. The developed model reveals the following facts: in the first service, advantageous locations for the servers are not symmetric between the advantage and deuce sides. Higher-ranked players can win more points than lower-ranked players even if their shots land in easy locations, that is, in the middle of the service court.
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